Machine and method for producing bevel gears

ABSTRACT

A machine for manufacturing bevel and hypoid gears comprising a machine column including a first side and a second side. A first spindle is movably secured to the first side with the first spindle being rotatable about a first axis. A second spindle is movably secured to the second side with the second spindle being rotatable about a second axis. The first and second spindles are movable linearly with respect to one another in up to three linear directions with at least one of the first and second spindles being angularly movable with respect to its respective side. The angular movement of at least one of the first and second spindles being about a respective pivot axis extending generally parallel with its respective side.

[0001] This application claims the benefit of U.S. ProvisionalApplication No. 60/269,328 filed Feb. 16, 2001.

FIELD OF THE INVENTION

[0002] The present invention is directed to gear manufacturing machinesand more particularly to machines for cutting and grinding bevel gears.

BACKGROUND OF THE INVENTION

[0003] In the production of gears, especially bevel gears, two types ofprocesses are commonly employed, generating processes and non-generatingprocesses.

[0004] Generating processes can be divided into two categories, facemilling (intermittent indexing) and face hobbing (continuous indexing).In generating face milling processes, a rotating tool is fed into theworkpiece to a predetermined depth. Once this depth is reached, the tooland workpiece are then rolled together in a predetermined relativerolling motion, known as the generating roll, as though the workpiecewere rotating in mesh with a theoretical generating gear, the teeth ofthe theoretical generating gear being represented by the stock removingsurfaces of the tool. The profile shape of the tooth is formed byrelative motion of the tool and workpiece during the generating roll.

[0005] In generating face hobbing processes, the tool and workpiecerotate in a timed relationship and the tool is fed to depth therebyforming all tooth slots in a single plunge of the tool. After full depthis reached, the generating roll is commenced.

[0006] Non-generating processes, either intermittent indexing orcontinuous indexing, are those in which the profile shape of a tooth ona workpiece is produced directly from the profile shape on the tool. Thetool is fed into the workpiece and the profile shape on the tool isimparted to the workpiece. While no generating roll is employed, theconcept of a theoretical generating gear in the form of a theoretical“crown gear” is applicable in non-generating processes. The crown gearis that theoretical gear whose tooth surfaces are complementary with thetooth surfaces of the workpiece in non-generating processes. Therefore,the cutting blades on the tool represent the teeth of the theoreticalcrown gear when forming the tooth surfaces on the non-generatedworkpiece.

[0007] Conventional mechanical gear generating machines for producingbevel gears comprise a work support mechanism and a cradle mechanism.During a generating process, the cradle carries a circular tool along acircular path about an axis known as the cradle axis. The cradlerepresents the body of the theoretical generating gear and the cradleaxis corresponds to the axis of the theoretical generating gear. Thetool represents one or more teeth on the generating gear. The worksupport orients a workpiece relative to the cradle and rotates it at aspecified ratio to the cradle rotation. Traditionally, conventionalmechanical cradle-style bevel gear generating machines are usuallyequipped with a series of linear and angular scales (i.e. settings)which assist the operator in accurately locating the various machinecomponents in their proper positions.

[0008] It is common in many types of conventional mechanicalcradle-style bevel gear generating machines to include an adjustablemechanism which enables tilting of the cutter spindle, and hence, thecutting tool axis, relative to the axis of the cradle (i.e. the cutteraxis is not parallel to the cradle axis). Known as “cutter tilt,” theadjustment is usually utilized in order to match the cutting toolpressure angle to the pressure angle of the workpiece, and/or toposition the cutting surfaces of the tool to appropriately represent thetooth surfaces of the theoretical generating gear. In some types ofconventional mechanical cradle-style bevel gear generating machineswithout a cutter tilt mechanism, the effects of cutter tilt may beachieved by an altering of the relative rolling relationship between thecradle and workpiece. This altering is also known as “modified roll.”

[0009] In the recent past, gear producing machines have been developedwhich reduce the number of machine settings necessary to orient a toolrelative to a workpiece. These machines replace some or all of thesettings and movements of the conventional mechanical cradle-stylemachine with a system of linear, rotational, and/or pivoting axes.

SUMMARY OF THE INVENTION

[0010] The present invention is directed to a machine for manufacturingbevel and hypoid gears comprising a machine column including a firstside and a second side. A first spindle is movably secured to the firstside with the first spindle being rotatable about a first axis. A secondspindle is movably secured to the second side with the second spindlebeing rotatable about a second axis. The first and second spindles aremovable linearly with respect to one another in up to three lineardirections with at least one of the first and second spindles beingangularly movable with respect to its respective side. The angularmovement of at least one of the first and second spindles being about arespective pivot axis extending generally parallel with its respectiveside.

BRIEF DESCRIPTION OF THE DRAWINGS

[0011]FIG. 1 is an isometric view of a first embodiment of the inventivegear manufacturing machine with the tool and workpiece disengaged.

[0012]FIG. 2 is an isometric view of the first embodiment of theinventive gear manufacturing machine showing a cutting tool engaged witha pinion.

[0013]FIG. 3 is a top view of the gear manufacturing machine of FIG. 2.

[0014]FIG. 4 is an isometric view of the first embodiment of theinventive gear manufacturing machine showing a cutting tool engaged witha ring gear.

[0015]FIG. 5 is a top view of the gear manufacturing machine of FIG. 4.

[0016]FIG. 6 illustrates a conventional mechanical cradle-style bevelgear generating machine with cutter tilt.

[0017]FIG. 7 is a schematic top view of a conventional mechanicalcradle-style bevel gear generator.

[0018]FIG. 8 is a schematic front view of a conventional mechanicalcradle-style bevel gear generator.

[0019]FIG. 9 is a side view of the tool in FIG. 8.

[0020]FIG. 10 is a schematic top view of the cutting tool and workpieceof the first embodiment of the present invention.

[0021]FIG. 11 is a view along the cutting tool axis of FIG. 10.

[0022]FIG. 12 illustrates pivot axis F referenced in a coordinate systembased on the reference plane of the cutting tool in the first embodimentof the present invention.

[0023]FIG. 13 shows the coordinate system of FIG. 12 and the coordinatesystem of the first embodiment of the inventive machine.

[0024]FIG. 14 shows the coordinate systems of the cutting tool,X_(c)-Z_(c), and the inventive machine, X-Z, in the first embodiment ofthe present invention.

[0025]FIG. 15 is a machine axes motion diagram for a pinion cut on themachine embodiment shown in FIGS. 1-3.

[0026]FIG. 16 illustrates a pivot axis placement associated with aworkpiece spindle.

[0027]FIG. 17 exemplifies an alternative form of the machine column.

[0028]FIG. 18 depicts vertical machine motion being associated with atool spindle.

[0029]FIG. 19 is a top view showing pivot mechanisms being included withboth tool and workpiece spindles.

[0030]FIG. 20 illustrates horizontal guides being located inward ofvertical guides for movement of a workpiece spindle.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

[0031] The details of the present invention will now be discussed withreference to the accompanying drawings which illustrate the presentinvention by way of example only. In the drawings, similar features orcomponents will be referred to by like reference numbers.

[0032] In the context of the present invention, the term “bevel” gearsis understood to be of sufficient scope to include those types of gearsknown as bevel gears, “hypoid” gears, as well as those gears known as“crown” or “face” gears.

[0033] A first embodiment of the inventive machine for manufacturingbevel gears is illustrated in FIGS. 1-5 and designated generally by 2.For ease in viewing the various machine components, FIGS. 1-5 illustratethe inventive machine without doors and exterior sheet metal. Themachine 2 comprises a single stationary column 4 of the type disclosedin U.S. Pat. No. 6,120,355, the disclosure of which is herebyincorporated by reference. Column 4 is preferably a monolithic structuresuch as cast iron but may be assembled from metal plates, for examplesteel plates, or may comprise individual frame elements such as cornerposts and frame elements positioned as appropriate to support machineguideways or other components. Column 4 comprises at least two sides,preferably four sides, with at least two of the sides, first side 6 andsecond side 8, being oriented at a desired angle, preferablyperpendicular, to one another although sides oriented at angles greaterthan or less than 90 degrees (see column 4 in FIG. 19, for example) arealso contemplated by the present invention. Each of the first and secondsides comprises a width and a height (as viewed in FIG. 1).Alternatively, monolithic column 4 may comprise a form having non-planarsides such as, for example, a generally cylindrical column asillustrated by FIG. 17.

[0034] First side 6 includes first spindle 10 having a front or seatingsurface 15. Spindle 10 is rotatable about axis Q and is preferablydriven by a direct drive motor 12, preferably liquid-cooled, andpreferably mounted behind front and rear spindle bearings (not shown).Spindle 10 is pivotably secured to a spindle support 11 which, alongwith spindle 10, is movable in direction Z along the width of first side6 on ways 14 attached to column 4. Movement of spindle 10 in direction Zis provided by motor 16 through a direct-coupled ballscrew (not shown)or by direct drive. Preferably, a cutting or grinding tool 18 (cuttingtool is shown) is releasably mounted to spindle 10 by suitable mountingequipment as is known in the art.

[0035] As stated above, first spindle 10 is attached to spindle support11 such that pivoting of the spindle, and hence the tool 18, may occurabout pivot axis F. Spindle bracket 13 is pivotally attached to support11 via at least one, and preferably two, bearing connections 20 and 22,upper bearing connection 20 and lower bearing connection 22. Pivoting ofspindle 10 is effected by motor 24 and direct-coupled ballscrew 26, orby direct drive, acting through sleeve portion 28 of yolk 30. Yolk 30 ispivotally attached to spindle 10 preferably at an upper connection 32and a lower connection 34 such that yolk 30 may angularly move relativeto spindle 10 about axis V. Advancing of ballscrew 26, and hence yolk30, effectively pushes drive motor 12 angularly away from column 4thereby causing a pivot motion about axis F to angularly move the tool18 toward the machine column 4. See FIG. 3 for cutting a pinion and FIG.5 for cutting a ring gear. Of course, retracting ballscrew 26 has theopposite effect. Alternatively, to effect pivoting of spindle 10, aslide movable on at least one guideway oriented in the Z direction andpositioned on spindle support 11 may be connected to spindle 10 or motor12 via a linkage mechanism. Movement of the slide on the guidewayeffects pivoting of spindle 10 about axis F. A further alternative is toinclude a motor at one or both of bearing connections 22 and 23 toeffect pivoting of spindle 10.

[0036] Second side 8 includes second spindle 40 which is rotatable aboutaxis N and is preferably driven by a direct drive motor 42, preferablyliquid-cooled, and preferably mounted behind front and rear spindlebearings (not shown). Spindle 40 is movable in direction X along thewidth of second side 8 on ways 44 attached to slide 46. Movement ofspindle 40 in direction X is provided by motor 48 through adirect-coupled ballscrew 49 or by direct drive. Preferably, a workpiece(a pinion 50 in FIG. 1 and a ring gear 51 in FIG. 4) is releasablymounted to spindle 40 by suitable workholding equipment 41 as is knownin the art. Spindle 40 is also movable in direction Y along the heightof second side 8 since slide 46 is movable in the Y direction via ways52 with movement being provided by motor 54 through a direct-coupledballscrew 55 or by direct drive. Directions X, Y and Z are preferablymutually perpendicular with respect to one another although one or moremay be inclined with respect to its perpendicular orientation. Forpurposes of illustration, in all Figures, the Y direction is vertical.

[0037] While the arrangement of ways 44 and 52 is preferred as shown inFIGS. 1-5, FIG. 20 illustrates an alternative but less preferredembodiment where ways 44 may be attached to side 8 with slide 46 beingmovable in the X direction on ways 44. Ways 52 may be arranged on slide46 and spindle 40 attached to ways 52 for movement in the Y direction.It is also contemplated that movement in the Y direction may be effectedby spindle 10 instead of spindle 40 (FIG. 18, with motors removed forclarity purposes).

[0038] The present invention makes possible, by use of a vertical columnas the common support for both the workpiece and tool spindles, pivotingof the spindle on which the tool resides as shown in FIGS. 1-5.Conventional pivoting of the workpiece spindle is also technicallypossible, as is shown in FIG. 16. Pivoting of the workpiece spindle,however, may require large pivot angles for ring gears resulting in adegradation of static and dynamic stiffness. With pinions, pivoting ofthe workpiece spindle is, at best, a compromise given that mountingdistances, arbor heights and pitch angles vary over a wide range withinpinions and even more when considering both pinions and ring gears.

[0039] Alternatively, both spindles 10, 40 may be pivoted as seen inFIG. 19 which shows a pivoting mechanism (e.g. yolk 30, 30′) attachedfor angular movement about axes (V, V′) to each spindle 10, 40. Whileeach spindle 10, 40 may actively pivot about respective pivot axes (F,F′) during manufacture of a gear, the present invention alsocontemplates one of the spindles 10, 40 being set at a predeterminedpivot angle prior to manufacture of a gear, or, one of the spindles 10,40 pivoting between incremental set positions during manufacture of agear. Movement between such incremental set positions may reduce theamount or magnitude of pivoting necessary by the other of the spindlesduring manufacture of the gear.

[0040] Movement of first spindle 10 in direction Z, second spindle 40 indirection X, second spindle 40 via slide 46 in direction Y, pivoting offirst spindle 10 about axis F, as well as first spindle 10 rotation andsecond spindle 40 rotation, is imparted by the separate drive motors 16,48, 54, 24, 12 and 42 respectively. The above-named components arecapable of independent movement with respect to one another or may movesimultaneously with one another. Each of the respective motors ispreferably associated a feedback device such as a linear or rotaryencoder, such as pivot axis encoder 23 (FIG. 1), as part of a CNC systemwhich governs the operation of the drive motors in accordance withinstructions input to a computer controller (i.e. CNC) such as the Fanucmodel 160i or Siemens model 840D (not shown).

[0041] The machine of the present invention as illustrated by theembodiments is guided by the controller which preferably continuouslyissues positioning and/or velocity commands to the various drive motors.Rather than load a large number of axis-positioning commands into thecontroller, it may be more efficient and meaningful to input a smallerset of data describing the gear manufacturing process. A logicalcandidate for such data is a set of “basic machine settings.” Using thisapproach, a machine operator would enter a set of basic machine settings(discussed in detail below) into the controller, which, in turn, wouldcalculate the axis positions corresponding to a range of cradlepositions. Thus, the basic “language” for describing bevel geargenerating motions is retained in the present invention.

[0042] The relationship between the theoretical generating gear in meshwith a workpiece is maintained in the present invention by angularmovement between the tool and workpiece axes in combination withrelative rectilinear movements between the tool and workpiece axes alongone or more of the three rectilinear axes and rotational movement of theworkpiece about its axis. In the case of continuous indexing, rotationalmovement of the tool axis is also controlled.

[0043] Because of the complexity of tooth surfaces formed byconventional mechanical cradle-style bevel gear generators, such toothsurfaces can only be exactly defined geometrically by the machinemotions which are used to produce them. While some general parameters ofgear design may be specified (e.g. number of teeth, pitch angle, etc.)the equations which are used to define bevel tooth surfaces are themotion equations of generating machines.

[0044] Given the above, it is evident that with each machine configureddifferently than the conventional mechanical cradle-style bevel geargenerator, a new set of formulas and other know-how would be required todetermine appropriate machine settings and operating parameters forproducing known gear tooth geometry and mating characteristics. However,since the conventional mechanical cradle-style bevel gear generatingmachine has been in existence for many years, a large amount of know-howalready exists which relates desired tooth geometry and matingcharacteristics to conventional cradle-style machine settings.

[0045] Therefore, although a new set of formulas may be developed for anewly configured machine, it has generally become the practice in theart to utilize the same input parameters as a conventional mechanicalcradle-style gear generating machine for other machines having adifferent number and/or configuration of axes. In other words, thepositions of the tool and workpiece axes in the coordinate system of aconventional mechanical cradle-style bevel gear generating machine aretransformed into the alternative coordinate system of the newlyconfigured machine. An example of such a transformation can be found inU.S. Pat. No. 4,981,402 the disclosure of which is hereby incorporatedby reference. The relationship between the invention and theconventional mechanical cradle-style bevel gear generator will bediscussed below.

[0046] A conventional mechanical cradle-style bevel gear generatingmachine 60 (FIG. 6) for producing bevel gears generally comprises amachine frame 62, work support mechanism 64 and a cradle support 66comprising a cradle mechanism 68. Traditionally, conventional mechanicalcradle-style bevel gear generating machines are usually equipped with aseries of linear and angular scales (i.e. settings) which assist theoperator in accurately locating the various machine components in theirproper positions. The following is a description of settings found on atilt-equipped conventional mechanical cradle-style bevel gear generatingmachine such as the machine shown in FIG. 6:

[0047] Eccentric Angle 70 controls the distance between the cradle axis,A_(C), and the tool axis, T,

[0048] Tool Spindle Rotation Angle 72 controls the angle between thecradle axis and the tool axis, commonly called the tilt angle,

[0049] Swivel Angle 74 controls the orientation of the tool axisrelative to a fixed reference on the cradle 88,

[0050] Cradle Angle 76 positions the tool 78 at some angular positionabout the cradle axis,

[0051] Root Angle 80 orients the work support 64 relative to the cradleaxis,

[0052] Sliding Base 82 is a linear dimension which regulates the depthof tool engagement with the workpiece,

[0053] Head Setting 84 is a linear adjustment of the work support 64along the workpiece axis, W, and,

[0054] Work Offset 86 controls the offset of the workpiece axis relativeto the cradle axis.

[0055] A final setting, ratio-of-roll, governs the relative rotationalmotion between the cradle 68 and workpiece 88. It should be noted thatsome of the above machine settings must be calculated taking intoaccount the following workpiece and tooling design specifications:

[0056] the mounting distance of the blank workpiece (symbol−M_(d)),

[0057] the overall length of the work holding equipment (symbol−A_(b)),and,

[0058] the overall height of the tool (symbol−h).

[0059] Although the measures of these settings allow precise positioningof the machine components, the measures themselves convey littleinformation about their location relative to one another. For instance,a head setting of 5 inches will position the work support in a differentphysical location relative to the cradle depending on the model ofmachine considered. This situation results from the “zero” head-settingposition being defined differently on different model machines. In asimilar manner, a setting of 30 degrees on the eccentric anglecommunicates little regarding the distance between the tool and thecradle axis since it is an angular measure which actually controls alinear dimension. Additional details must be furnished before the moremeaningful linear distance can be calculated.

[0060] More immediately significant to the artisan is a set of absolutemeasures of machine component positioning, that is, measures which areindependent of the tooling or machine model considered. These general,or basic machine settings, immediately communicate a sense of size andproportion regarding the generating gear and the workpiece beinggenerated. They also provide a common starting point for gear design.For example, gear sets may be designed in terms of basic settings, thusunifying design procedures among many models of machines. In addition,analysis procedures need be written only once to cover all machineconfigurations if basic settings are employed. Of course, conversion totrue machine-dependent settings is required to set-up a conventionalmechanical cradle-style bevel gear generator but this is best performedjust before presentation as a machine set-up summary.

[0061] A description of basic machine settings appears below and withreference to FIGS. 7-9. FIGS. 7 and 8 show, respectively, top and frontviews of a conventional mechanical cradle-style bevel gear generatorwith tilt. FIG. 9 is a projection showing a side view of the tool intrue length. Details unrelated to the present discussion have beenomitted for clarity.

[0062] Initially, two reference points are defined. The first point,point C_(T), is on the tool axis at some known position relative to thetool. This point, called the Tool Center, is usually chosen to lie inthe plane defined by the tips of the tool (FIG. 9). The second referencepoint, CP, lies on the workpiece axis at the crossing point, that is,the point of intersection of the workpiece axis and the axis of itsmating member. In the case of hypoid gears, CP lies at the point ofapparent intersection between mating members when viewed in a planeparallel to both axes. Another point of interest, point O, is known asthe machine center. This point is defined by the intersection of thecradle axis and the plane of cradle rotation (FIG. 7).

[0063] Using the above points, the following basic settings may bedefined:

[0064] Radial, s, (FIG. 8)—the distance from machine center O to toolcenter C_(T) when viewed in the plane of cradle rotation.

[0065] Cradle Angle, q, (FIG. 8)—the angle formed by radial OC_(T) and aplane parallel to both the workpiece and cradle axes.

[0066] Tilt Angle, i, (FIG. 9)—the angle formed by the tool axis andcradle axis. Usually taken to be between 0 and 90 degrees.

[0067] Swivel Angle, j, (FIG. 8)—determines the direction of tool axistilt. It is measured from line C_(T)A which is rigidly connected andperpendicular to radial line OC_(T). Its measure is the angle formed byline C_(T)A and the projection of the tool axis on the plane of cradlerotation.

[0068] Work Offset, E_(m), (FIG. 8)—the minimum distance between thecradle axis and workpiece axis.

[0069] Sliding Base, X_(b), (FIG. 7)—the distance between machine centerO and point H, the point of apparent intersection of workpiece andcradle axes. This appears true length when viewed in a plane parallel toboth cradle and workpiece axes.

[0070] Head setting, X_(p), (FIG. 7)—the distance between apparent pointH (identified above) and crossing point CP. Measured along the workpieceaxis.

[0071] Root Angle, γ, (FIG. 7)—the angle formed by the workpiece axisand the plane of cradle rotation.

[0072] Note: All parameters appear true length in the noted Figures, andpositive in the sense shown.

[0073] The generation process is mainly governed by the ratio-of-roll(ratio of workpiece rotation to cradle rotation). Additional motionparameters (e.g. helical motion) may also be defined to augment therolling motion between the cradle and workpiece. It is noted that otherarrangements of basic machine settings could have been chosen instead ofthe one described. However, this particular choice of settings retains alikeness with conventional mechanical cradle-style bevel gear generatingmachine configurations, and clarifies essential geometric propertieswhere appropriate.

[0074] Besides the eight settings defined above, it is useful to measurethe rotational position of the workpiece about its own axis from somereference. Also, in the case of face hobbing, the rotary position of thetool about its own axis may be of interest. Combined together, these tenparameters totally describe the relative positioning between tool andworkpiece at any instant. Three of them (cradle angle, workpiecerotation, tool rotation) change in the process of generation, while theother seven are “true” settings, i.e. they usually remain fixed.

[0075] A mathematical model is developed which accepts the basic machinesettings, identified above, and exactly replicates bevel gear generationon the inventive embodiments through displacements along or about itssix axes. FIG. 10 and 11 show, respectively, partial front and top viewsof the inventive tool and workpiece arrangement in the coordinate systemof the first embodiment of the present invention. Referring to FIGS.7-9, which illustrate the tool and workpiece arrangement of aconventional mechanical cradle-style bevel gear generating machine inthe coordinate system of that conventional machine, vectors are definedalong the workpiece and tool axes: $\begin{matrix}{{\cdot \overset{\rightarrow}{p}} = \left\{ {{{- \cos}\quad \gamma},0,{{- \sin}\quad \gamma}} \right\}} & \text{workpiece~~axis} \\{{\cdot \overset{\rightarrow}{c}} = \left\{ {{\sin \quad i\quad {\sin \left( {q - j} \right)}},\quad {\sin \quad i\quad {\cos \left( {q - j} \right)}},{\cos \quad i}} \right\}} & \text{tool~~axis}\end{matrix}$

[0076] Next, the “key-way” vector, perpendicular and attached to theworkpiece and tool axes, are defined: $\begin{matrix}{{\cdot \overset{\rightarrow}{a}} = \left\{ {{{- \sin}\quad \gamma},\quad 0,{\cos \quad \gamma}} \right\}} & \text{workpiece~~key-way~~vector} \\{{\cdot \overset{\rightarrow}{b}} = \left\{ {{\cos \left( {q - j} \right)},{- {\sin \left( {q - j} \right)}},0} \right\}} & \text{tool~~key-way~~vector}\end{matrix}$

[0077] Finally, a vector R is defined from the tool seat T_(R) (the backof the tool) to the point W_(R) on the workpiece axis which liesdirectly in the seating surface plane of the work arbor:

{right arrow over (R)}={−s cos q, s sin q−E _(m) , X _(b)}−(X _(p) +M_(d) +A _(b)){right arrow over (p)}+h{right arrow over (c)}

[0078] Motions of the machine embodiment of FIGS. 1-5 may now bedetermined. A new coordinate system is associated with the axesarrangement of the orthogonal machine of FIGS. 1-5 with the origin beingat point W_(R) on the seating surface or nose 43 of the machine spindle40 Orthogonal axes are given by: $\begin{matrix}{{\cdot {\overset{\rightarrow}{u}}_{X}} = \overset{\rightarrow}{p}} & {\text{workpiece~~axis,~~lines~~up~~with~~}\text{X}\text{~~axis}} \\{{\cdot {\overset{\rightarrow}{u}}_{Y}} = {- \frac{\overset{\rightarrow}{p} \times \overset{\rightarrow}{c}}{{\overset{\rightarrow}{p} \times \overset{\rightarrow}{c}}}}} & {\text{vertical,~~pointing~~up,~~lines~~up~~with~~}\text{Y}\text{~~axis}} \\{{\cdot {\overset{\rightarrow}{u}}_{Z}} = {{\overset{\rightarrow}{u}}_{X} \times {\overset{\rightarrow}{u}}_{Y}}} & {\text{horizontal~~and~~perpendicular~~to}\quad u_{x}\text{,~~lines~~up}} \\\quad & {\text{with~~}\text{Z~~}\text{axis}}\end{matrix}$

[0079] Since pivot axis, F, as shown in FIGS. 1-5 is not located on theworkpiece axis, as is customary, but instead is preferably positioned inthe vicinity of the tool as shown by vector Δ₁ in FIG. 10, the positionof the pivot axis in the new coordinate system must be defined.

[0080] With reference to FIGS. 12 and 13, pivot axis F is defined in acoordinate system attached to tool 18 in which the axis Z_(C) iscoincident with the axis {right arrow over (c)} of the cutting tool andaxis X_(C) is perpendicular to Z_(C) and extends along the back surfaceof the tool 18 (FIG. 12). The following can be seen from FIG. 12:$\begin{matrix}{{\cdot {\overset{\rightarrow}{u}}_{ZC}} = \overset{\rightarrow}{c}} & {\text{unit~~vector}\quad u_{ZC}\quad \text{in~~the~~direction~~of}\quad Z_{C}} \\{{\cdot {\overset{\rightarrow}{u}}_{XC}} = {{\overset{\rightarrow}{u}}_{y} \times {\overset{\rightarrow}{u}}_{ZC}}} & {\text{unit~~vector}\quad u_{XC}\quad \text{in~~the~~direction~~of~~}X_{C}} \\{{\cdot {\overset{\rightarrow}{\Delta}}_{C}} = \left\{ {{\Delta \quad x_{C}},0,{\Delta \quad z_{C}}} \right\}} & \quad\end{matrix}$

[0081] As seen in FIG. 13, transformation of {right arrow over (Δ)}_(C)in the tool coordinate system of FIG. 12 to the new coordinate system ofthe embodiment shown in FIGS. 1-5 is given by: $\begin{matrix}{{{\cdot {\overset{\rightarrow}{\Delta}}_{1}} = \quad {{\left( {B - 180^{\circ}} \right)_{y} \cdot {\overset{\rightarrow}{\Delta}}_{C}}\quad {and}}},{therefore},} \\{{\cdot {\overset{\rightarrow}{\Delta}}_{1}} = \quad {{\left( \quad \begin{matrix}{\cos \left( {B - 180^{\circ}} \right)} & 0 & {\sin \left( {B - 180^{\circ}} \right)} \\0 & 1 & 0 \\{- {\sin \left( {B - 180^{\circ}} \right)}} & 0 & {\cos \left( {B - 180^{\circ}} \right)}\end{matrix}\quad \right)\begin{Bmatrix}{\Delta \quad x_{C}} \\0 \\{\Delta \quad z_{C}}\end{Bmatrix}} =}} \\{\quad \begin{Bmatrix}{{{- \Delta}\quad x_{C}\cos \quad B} - {\Delta \quad z_{C}\sin \quad B}} \\0 \\{{\Delta \quad x_{C}\sin \quad B} - {\Delta \quad z_{C}\cos \quad B}}\end{Bmatrix}}\end{matrix}$

[0082] From the coordinate system of FIGS. 10 and 11, which representsthe coordinate system of the embodiment illustrated in FIGS. 1-5, it maybe seen that:${\cdot {\overset{\rightarrow}{R}}_{1}} = {{\begin{Bmatrix}{\overset{\rightarrow}{R} \cdot {\overset{\rightarrow}{u}}_{X}} \\{\overset{\rightarrow}{R} \cdot {\overset{\rightarrow}{u}}_{Y}} \\{\overset{\rightarrow}{R} \cdot {\overset{\rightarrow}{u}}_{Z}}\end{Bmatrix}\quad {and}\quad {\overset{\rightarrow}{R}}_{2}} = {{\overset{\rightarrow}{\Delta}}_{1} - {\overset{\rightarrow}{R}}_{1}}}$

[0083] wherein:

[0084] R₁=vector from point T_(R) on tool to point W_(R) on the seatingsurface 43 of machine spindle 40, and,

[0085] R₂=vector from point W_(R) on the seating surface 43 of machinespindle 40 to pivot axis F.

[0086] Therefore, the displacement along the X, Y, Z rectilinear axes ofthe machine embodiment of FIGS. 1-5 at a specified increment, such aseach increment of generating roll, are calculated: $\begin{matrix}{{\cdot A_{X}} = R_{2_{X}}} & {\text{displacement~~along~~}\text{X}\text{~~axis}} \\{{\cdot A_{Y}} = {\overset{\rightarrow}{R}}_{2_{Y}}} & {\text{displacement~~along~~}\text{Y}\text{~~axis}} \\{{\cdot A_{Z}} = {\overset{\rightarrow}{R}}_{2_{Z}}} & {\text{displacement~~along~~}\text{Z}\text{~~axis}}\end{matrix}$

[0087] The three angular rotations must also be found. The pivot angle,B, at a specified increment, such as each increment of generating roll,is given by:${\cdot B} = {\arccos \left( {{- \overset{\rightarrow}{p}} \cdot \left( {\frac{\overset{\rightarrow}{p} \times \overset{\rightarrow}{c}}{{\overset{\rightarrow}{p} \times \overset{\rightarrow}{c}}} \times \overset{\rightarrow}{c}} \right)} \right)}$

[0088] The tool and workpiece axes each have an associated rotationalphase angle which is superimposed on their motions as defined byconventional mechanical generators. These compensate for the changingrelative orientation of conventional and inventive machine horizontalplanes at a specified increment, such as each increment of generatingroll. They are defined as: $\begin{matrix}{{\cdot \alpha} = {\arcsin \left( {{- \overset{\rightarrow}{a}} \cdot \frac{\overset{\rightarrow}{p} \times \overset{\rightarrow}{c}}{{\overset{\rightarrow}{p} \times \overset{\rightarrow}{c}}}} \right)}} & \text{workpiece~~axis~~phase~~angle} \\{{\cdot \beta} = {\arcsin \left( {{- \overset{\rightarrow}{b}} \cdot \left( {\frac{\overset{\rightarrow}{p} \times \overset{\rightarrow}{c}}{{\overset{\rightarrow}{p} \times \overset{\rightarrow}{c}}} \times \overset{\rightarrow}{c}} \right)} \right)}} & \text{tool~~axis~~phase~~angle}\end{matrix}$

[0089] An operation is also performed to determine the desiredrotational position of the workpiece, ω, in accordance with phase anglesalpha and beta and other setup constants including ratio of roll, R_(a),which specifies the ratio of relative rotation between the imaginarycradle and workpiece required for generation, indexing or hobbingconstant, R_(C), which specifies the ratio of relative rotation betweenthe tool and workpiece for continuous indexing, and reference constantω₀ which specifies a known rotational position between the tool andworkpiece. Other constants (not shown) may be used to further adjust theworkpiece axis rotational position for duplicating special motions ofconventional mechanical cradle-style machines such as “modified roll.”The operation may be expressed as:

ω=ω_(O) +f(R _(a) ,Δq)+f(R _(C) ,Δt)+f(R _(C), beta)+alpha

[0090] wherein:

[0091] Δq=q−q₀

[0092]  with

[0093] q=instantaneous cradle roll orientation

[0094] q₀=cradle orientation at center of roll

[0095] Δt=t−t₀

[0096]  with

[0097] t=instantaneous tool spindle orientation

[0098] t₀=initial tool spindle orientation

[0099] The above equation as written represents one embodiment of thegeneral mathematical relationship wherein workpiece rotation is afunction of R_(a), R_(C), alpha, beta, q and t. However, other variablessuch as intermediate variables in the form of basic settings s, i, j,E_(m), X_(b), X_(p), and γ, for example, may also be utilized indescribing workpiece rotation resulting from input parameters. Thecalculation for ω is not limited to the specific expression shown abovefor this embodiment.

[0100] It has been discovered that the pivot axis F, defined, forinstance with respect to cutting tools, within the cutting toolreference plane coordinate system X_(CR)-Z_(CR) of FIG. 14, ispreferably located in the quadrant of that coordinate system whereX_(CR) is positive and Z_(CR) values are negative. Axis X_(CR) lies inthe cutter reference plane 92 defined by the mid-point of the height ofthe blade cutting edges and axis Z_(CR) is coincident with the tool axis{right arrow over (c)}. Applying this definition to the embodiment ofFIG. 1, for example, with axis Q perpendicular with axis N, it can beseen that the pivot axis F should be located on or “behind” thereference plane of the cutting tool 18 and at a point between the axis Qand the machine column 4. Although the above positioning of the pivotaxis is preferred, placement of the pivot axis along axis Q or outwardfrom axis Q away from machine column 4 may be included in the presentinvention.

[0101] Placement of the pivot axis F should preferably be at a locationwhereby smooth and minimal motion along the axes is exhibited, such asnoted on motion diagrams utilized to analyze machine motions, along withfew, if any, reversal or inflection points. Preferably, pivot axis Fshould be positioned in the quadrant discussed above at a locationtherein defined by a positive ΔX_(CR) value being equal to the averageradius of the cutting tool(s) to be used on the machine. Preferably,ΔZ_(CR) is equal to zero. For example, if cutting tools having diametersof 3 inches and 9 inches are contemplated, the average radius of thecutting tools would be 3 inches. Thus, ΔX_(CR) would be 3 inches,placing it at about point G in FIG. 14 if, for example, cutting tool 18has a radius of 4.5 inches. Point G is in the vicinity of the gear toothcalculation point (for the average pinion or ring gear) which is locatedat the center of a tooth. A pivot axis passing through point G would beperpendicular to the X_(CR)-Z_(CR) plane.

[0102] Also preferred is placement of the pivot axis in a location thatallows the pivoting mechanism to be isolated from the workpiece andtool, such that it can be shielded from stray chips. Isolating the pivotaxis should preferably still permit minimal and smooth motion along theaxes with few, if any, reversal or inflection points as noted on machinemotion diagrams as was discussed above. Given this, it has been foundthat one preferred location for the pivot axis F is at a point ΔX_(CR)located between the cutting blades of the largest tool contemplated forthe machine and the machine column 4, and at a ΔZ_(CR) generally aboutequal in magnitude to ΔX_(CR). More specifically, ΔX_(CR) is preferablyat about the average diameter of the tools contemplated for the machineand ΔZ_(CR) is preferably generally about equal in magnitude to ΔX_(CR).For example, if cutting tools of 3 inch diameter and 9 inch diameter arecontemplated, the average diameter is 6 inches. Thus, ΔX_(CR)=6 inches,placing it beyond the cutting blades of the largest tool which would beat ΔX_(CR)=4.5 inches for the 9 inch diameter tool. ΔZ_(CR) would alsobe generally about 6 inches but may vary plus/minus 2 inches. Withplacement of the pivot axis as set forth, travel of about 10-30 mm isnoted along each of the linear axes which is desirably small and yet ofa magnitude such that motion along the axes is accurately controllableby the machine controls.

[0103] As an example, a 12 tooth pinion having a pitch angle of 28.73°and a spiral angle of 50.0° is produced by generated face hobbing on amachine as shown in FIGS. 1-3. The basic settings for the machine wereas follows: s = 135.82 radial q = 65.83 center of roll i = 31.79 tiltangle j = 320.26 swivel angle E_(m) = 48.2638 offset X_(p) = −0.0091head setting X_(b) = 34.6578 slide base offset gamma (γ) = −0.01 rootangle M_(d) = 116.84 mounting distance A_(b) = 139.7 arbor height h =101.6 tool height BN = 17 number of blade groups on the cutting toolR_(a) = 3.58335 ratio of roll

[0104] The hobbing or index constant, R_(C), is defined by the ratio ofthe number of blade groups on the cutting tool divided by the number ofteeth on the workpiece. Therefore:

R _(C) =BN/no.teeth_(workpiece)=17/12

[0105] Additional machine constants (see FIG. 12):

[0106] ΔX_(C)=152.4 mm

[0107] ΔZ_(C)=−76.2 mm

[0108] Looking at the machine axes motion diagram of FIG. 15, it isshown that during the generation of the face hobbed pinion describedabove, there was about 20 mm of motion along each of the Z and Y axesand about 30 mm of motion along the X axis. It is also noted thatrotation about the pivot axis F was about 0.5 degree. No points ofinflection or reversal for any axes are noted on the diagram.

[0109] Conventionally, the workpiece is pivoted relative to the base.The introduction of the use of a single column to support both the toolspindle and the workpiece spindle now allows the tool spindle to bepivoted relative to the column. It may also be possible, however, forcertain applications, to pivot the workpiece spindle either alone or inconjunction with pivoting the tool spindle.

[0110] It is to be understood that although the present invention hasbeen discussed and illustrated with respect to a cutting machine, thepresent invention is also understood to equally encompass a grindingmachine for bevel gears.

[0111] While the invention has been described with reference topreferred embodiments it is to be understood that the invention is notlimited to the particulars thereof. The present invention is intended toinclude modifications which would be apparent to those skilled in theart to which the subject matter pertains.

What is claimed is:
 1. A machine for manufacturing bevel and hypoidgears comprising: a column; a workpiece spindle movably mounted to saidcolumn; a tool spindle movably mounted to said column; said workpiecespindle and said tool spindle being translatable with respect to oneanother in up to three different directions; said workpiece spindle andsaid tool spindle being angularly movable with respect to one anotheraround at least one vertical pivot axis.
 2. The machine of claim 1,wherein said three different directions are mutually perpendicular toone another.
 3. The machine of claim 1, wherein only one of saidworkpiece spindle and said tool spindle is angularly movable withrespect to said column.
 4. The machine of claim 1, wherein said toolspindle moves linearly in a first of said three different directions andsaid workpiece spindle moves linearly in a second and a third of saidthree different directions.
 5. The machine of claim 1, further includingsaid tool spindle being supported for angular movement about said atleast one vertical pivot axis by at least two bearings with one of thebearings being located above said tool spindle and the other of thebearings being located below said tool spindle.
 6. The machine of claim5, wherein said tool spindle has a tool spindle axis and said at leastone vertical pivot axis is located in the region defined between saidtool spindle axis and said column.
 7. The machine of claim 6, whereinsaid at least one vertical pivot axis is located in the region behind areference plane of a tool mounted on said tool spindle.
 8. A method ofmachining bevel and hypoid gears on a machine including a column, aworkpiece spindle movably secured to said column, and a tool spindlemovably secured to said column, said method comprising: mounting a toolon said tool spindle; mounting a workpiece on said workpiece spindle;rotating said tool around a tool axis; rotating said workpiece around aworkpiece axis; moving one of said workpiece spindle and said toolspindle relative to said column in a vertical direction; moving one ofsaid workpiece spindle and said tool spindle relative to said column ina first horizontal direction; moving one of said workpiece spindle andsaid tool spindle relative to said column in a second horizontaldirection; pivoting at least one of said workpiece spindle and said toolspindle relative to said column around at least one vertical pivot axis;and engaging said tool with said workpiece to machine a tooth slot insaid workpiece.
 9. The method of claim 8, wherein said tool spindlepivots around said at least one vertical pivot axis and said at leastone vertical pivot axis is located between said tool axis and saidcolumn.
 10. The method of claim 8, wherein engaging said tool with saidworkpiece includes machining all tooth slots in said workpiece withoutdisengaging said tool from said workpiece.
 11. A machine formanufacturing bevel and hypoid gears comprising: a column; a workpiecespindle; a tool spindle; means for movably supporting said workpiecespindle and said tool spindle on said column for relative translationalmovement along first, second, and third linear directions; and means forpivotably supporting at least one of said workpiece spindle and saidtool spindle for relative angular movement.
 12. The machine of claim 11,wherein said column is a stationary monolithic column having first andsecond substantially vertical surface areas.
 13. The machine of claim12, wherein said means for movably supporting said workpiece spindle andsaid tool spindle includes means for movably supporting said workpiecespindle on said first substantially vertical surface area for movementof said workpiece spindle along a vertical direction and a firsthorizontal direction and means for movably supporting said tool spindleon said second substantially vertical surface area for movement of saidtool spindle along a second horizontal direction.
 14. The machine ofclaim 13, wherein said means for pivotably supporting at least one ofsaid workpiece spindle and said tool spindle includes a pivot connectedto said tool spindle to allow movement of said tool spindle around avertical pivot axis.